1. Date of download: 10/13/2017
Copyright © ASME. All rights reserved.
From: Batch Process and Sensitivity Analysis of Collision Detection of Planar Convex Polygons in Motion
J. Comput. Inf. Sci. Eng. 2013;13(4): doi: /
Figure Legend:
The growth model and growth distance [12]. The original shape of each object is in gray; and its growth model (similar to its original shape) is in white. Three possible proximal relations between the two objects: (a) separate (d > 1), (b) just in contact (d = 1), or (c) interfered (d < 1).

2. Date of download: 10/13/2017
Copyright © ASME. All rights reserved.
From: Batch Process and Sensitivity Analysis of Collision Detection of Planar Convex Polygons in Motion
J. Comput. Inf. Sci. Eng. 2013;13(4): doi: /
Figure Legend:
A convex polygon can be expressed as the convex combination of the vectors pointing from a seed point pk to each vertex of the polygon. The motion of this object can be uniquely addressed, in the sense of kinematics, by its translational degrees of freedom pk(t) and rotational degree of freedom θK(t).

3. Date of download: 10/13/2017
Copyright © ASME. All rights reserved.
From: Batch Process and Sensitivity Analysis of Collision Detection of Planar Convex Polygons in Motion
J. Comput. Inf. Sci. Eng. 2013;13(4): doi: /
Figure Legend:
The growth distance of two polygons is determined by their relative configuration regardless their global coordinates

4. Date of download: 10/13/2017
Copyright © ASME. All rights reserved.
From: Batch Process and Sensitivity Analysis of Collision Detection of Planar Convex Polygons in Motion
J. Comput. Inf. Sci. Eng. 2013;13(4): doi: /
Figure Legend:
The change in the relative configuration between two convex polygons (in gray) is a kinematic combination of a pure translation Δp˜(t) and a pure rotation Δθ˜(t). (a) The initial configurations of OA and OQ, together with their growth models outlined in a just-contact condition. The change in the relative configuration is kinematically equivalent to either (b) the translation-first and rotation-second sequence Q1 → Q2 → Q3, or (c) the rotation-first and translation-second sequence Q1 →Q3 → Q2.

5. Date of download: 10/13/2017
Copyright © ASME. All rights reserved.
From: Batch Process and Sensitivity Analysis of Collision Detection of Planar Convex Polygons in Motion
J. Comput. Inf. Sci. Eng. 2013;13(4): doi: /
Figure Legend:
Illustration of the two-step decomposition procedure for the change in the relative configuration of two moving convex polygons OA and OQ by a translation-rotation sequence (Q1 → Q2 → Q3). (a) Q1 → Q2 is a kinematic translation Δp˜(t), whereby the growth models OAT and OQT are scaled to be just in contact. The growth distance is l2/l1, where l1 and l2 are the size index to their original and “grown” shapes, respectively. (b) Q2 → Q3 is a kinematic rotation Δθ˜(t). Their growth distance is l3/l2.

6. Date of download: 10/13/2017
Copyright © ASME. All rights reserved.
From: Batch Process and Sensitivity Analysis of Collision Detection of Planar Convex Polygons in Motion
J. Comput. Inf. Sci. Eng. 2013;13(4): doi: /
Figure Legend:
Example. (a) The initial configurations of two square objects. (b) dTrans is an unbounded, convex function of Δp˜ = [Δx˜,Δy˜] and has a minimum 0 at Δp˜ = [4,7] where the only vertex locates. (c) The projection of dTrans. The path ABC is used for the illustration in Fig. 7. (d) dRot has a periodicity of 180 deg for this example.

7. Date of download: 10/13/2017
Copyright © ASME. All rights reserved.
From: Batch Process and Sensitivity Analysis of Collision Detection of Planar Convex Polygons in Motion
J. Comput. Inf. Sci. Eng. 2013;13(4): doi: /
Figure Legend:
The change in the relative translation of two square objects (in gray) follows the path ABC defined in Fig. 6(c). The growth models are shown in white. (a) The growth models of the two objects, subject to the “just in contact” condition, remain unchanged along the path from A to B. The growth models are in point-contact in configurations A and B, while in line-contact between A and B. (b) and (c) As the relative translation follows the path from B to C, the growth models is expanded until they are just in contact to each other.